Existence and exponential decay estimates for an N -dimensional nonlinear wave equation with a nonlocal boundary condition

Boundary value problems

Nguyen Thanh Long¹  Nguyen Anh Triet²  Le Thi Phuong Ngoc³ 

[1] Department of Mathematics and Computer Science, University of Natural Science, Vietnam National University Ho Chi Minh City, Ho Chi Minh City, Vietnam;Department of Mathematics, University of Architecture of Ho Chi Minh City, Ho Chi Minh City, Vietnam;University of Khanh Hoa, Nha Trang City, Vietnam

关键词: Galerkin method;    nonlinear wave equation;    local existence;    global existence;    exponential decay;    35L05;    35L15;    35L70;    37B25;   

DOI  :  10.1186/s13661-016-0527-5

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

Motivated by the recent known results as regards the existence and exponential decay of solutions for wave equations, this paper is devoted to the study of an N-dimensional nonlinear wave equation with a nonlocal boundary condition. We first state two local existence theorems. Next, we give a sufficient condition to guarantee the global existence and exponential decay of weak solutions. The main tools are the Faedo-Galerkin method and the Lyapunov method.

【 授权许可】

CC BY